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# Percents for Nursing School Entrance Exam Study Guide (page 3)

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Updated on Aug 12, 2011

### Percent Word Problems

Word problems involving percents come in three main varieties:

• Find a percent of a whole.
• Example: What is 30% of 40?

• Find what percent one number is of another number.
• Example: 12 is what percent of 40?

• Find the whole when the percent of it is given.
• Example: 12 is 30% of what number?

While each variety has its own approach, there is a single shortcut formula you can use to solve each of these:

The is is the number that usually follows or is just before the word is in the question.

The of is the number that usually follows the word of in the question.

The % is the number that is in front of the % or percent in the question. Or you may think of the shortcut formula as:

To solve each of the three varieties, we're going to use the fact that the cross products of these two functions are always equal. The cross products are the products of the numbers diagonally across from each other. Remembering that product means multiply, here's how to create the cross products for the percent shortcut:

Here's how to use the shortcut with cross products:

 Find a percent of a whole. What is 30% of 40? 30 is the % and 40 is the of number: Cross multiply and solve for is: is × 100 = 40 × 30 is × 100 = 1,200 12 × 100 = 1,200

Thus, 12 is 30% of 40.

 Find what percent one number is of another number. 12 is what percent of 40? 12 is the is number and 40 is the of number: Cross multiply and solve for %: 12 × 100 = 40 × % 1,200 = 40 × % 1,200 = 40 ×30

Thus, 12 is 30% of 40.

 Find the whole when the percent of it is given. 12 is 30% of what number? 12 is the is number and 30 is the %: Cross multiply and solve for the of number: 12 × 100 = of ×30 1,200 = of × 30 1,200 = 40 ×30

Thus, 12 is 30% of 40.

You can use the same technique when asked to find a percent increase or decrease. The is number is the actual increase or decrease, and the of number is the original amount.

Example: If a merchant puts his \$20 hats on sale for \$15, by what percent does he decrease the selling price?
1. Calculate the actual decrease, the is number:                               \$20 – \$15 = \$5
2. The of number is the original amount,                                          \$20.
3. Set up the equation and solve for of by cross multiplying:
4.                                                                                                   5 × 100 = 20 × %

500 = 20 × %

500 = 20 × 25

5. Thus, he decreased the selling price by 25%.

If the merchant later raises the price of the hats from \$15 back to \$20,

don't be fooled into thinking that the percent increase is also 25%! It's                 5 × 100 = 15 × %

actually more, because the increase amount of \$5 is now based on a lower           500 = 15 × %

original price of only \$15:                                                                                     500 = 15 ×

Thus, the selling price is increased by 33%.

The practice quiz for this study guide can be found at:

Mathematics for Nursing School Entrance Exam Practice Problems